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ON CERTAIN TOPOLOGICAL INDICES OF THE DERIVED GRAPHS OF SUBDIVISION GRAPHS

Yıl 2016, Cilt: 6 Sayı: 2, 324 - 332, 01.12.2016

Öz

The derived graph [G]y of a graph G is the graph having the same vertex set as G, with two vertices of [G]y being adjacent if and only if their distance in G is two. Topological indices are valuable in the study of QSAR/QSPR. There are numerous applications of graph theory in the eld of structural chemistry. In this paper, we compute generalized Randic, general Zagreb, general sum-connectivity, ABC, GA; ABC4, and GA5 indices of the derived graphs of subdivision graphs.

Kaynakça

  • Ashrafi,A.R., Doˇsli´c,T., and Hamzeh,A., (2010), The Zagreb coindices of graph operations, Discrete Appl. Math., 158, pp. 1571–1578.
  • Basavanagoud,B., Gutman,I. and Gali,C.S., (2015), On second Zagreb index and coindex of some derived graphs, Kragujevac J. Sci., 37, pp. 113–121.
  • Doˇsli´c,T., (2008), Vertex-weighted Wiener polynomials for composite graphs, Ars Mathematica Con- tempooranea, 1, pp. 66–80.
  • Estrada,E., Torres,L., Rodriguez,L. and Gutman,I., (1998), An atom-bond connectivity index: Mod- elling the enthalpy of formation of alkanes. Indian J. Chem., 37A, pp. 849–855.
  • Furtula,B., Graovac,A. and Vukiˇcevi´c,D., (2010), Augmented Zagreb index. Journal of Mathematical Chemistry., 48, pp. 370–380.
  • Ghorbani,M. and HosseinzadehM.A., (2010), Computing ABC4index of nanostar dendrimers, Opto- electron. Adv. Mater.-Rapid Commun., 4(9), pp. 1419–1422.
  • Graovac,A., Ghorbani,M. and Hosseinzadeh,M.A., Computing fifth geometric-arithmetic index for nanostar dendrimers., J. Math. Nanosci, 1, pp. 33–42.
  • Gutman,I. and Trinajsti´c,N., (1972), Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17, pp. 535–538.
  • Gutman,I., (1994), Selected properties of the Schultz molecular topological index, J. Chem. Inf. Com- put. Sci., 34, pp. 1087–1089.
  • Gutman,I., Furtula,B. and Elphick,C., (2014), Three new/old vertexdegreebased topological indices, MATCH Commun. Math. Comput. Chem., 72, pp. 617–632.
  • Hande,S.P., Jog,S.R., Ramane,H.S., Hampiholi,P.R., Gutman,I. and Durgi,B.S., (2013), Derived graphs of subdivision graphs, Kragujevac J. Sci., 37(2), pp. 319–323.
  • Harary,F., (1969), Graph Theory, Addison–Wesely, Reading.
  • Hosamani,S.M. and Gutman,I., (2014), Zagreb indices of transformation graphs and total transfor- mation graphs, Appl. Math. Comput., 247, pp. 1156-1160.
  • Hosamani,S.M. and Basavanagoud,B., (2015), New upper bounds for the first Zagreb index, MATCH Commun. Math. Comput. Chem., 74(1), pp. 97–101.
  • Li,X. and Shi,Y., (2008), A survey on the Randi´c index, MATCH Commun. Math. Comput. Chem., 59(1), pp. 127-156.
  • Li,X. and Zhao,H., (2004), Trees with the first three smallest and largest generalized topological indices, MATCH Commun. Math. Comput. Chem., 50, pp. 57-62.
  • Nadeem,M.F., Zafar,S. and Zahid,Z., (2015), Certain topological indicies of the line graph of subdiv- sion graphs, Appl. Math. Comput., (271), pp. 790–794.
  • Randi´c,M., (1974), On characterization of molecular branching, J. Am. Chem. Soc., 97, pp. 6609–6615. [19] Ranjini,P.S., Lokesha,V. and Cangul,I.N., (2011), On the Zagreb indices of the line graphs of the subdivision graphs, Appl. Math. Comput., 218, pp. 699–702.
  • Ranjini,P.S., Lokesha,V. and Rajan,M.A., (2011), On the Shultz index of the subdivision graphs, Adv. Stud. Contemp. Math., 21(3), pp. 279-290.
  • Shirdel,G.H., Rezapour,H. and Sayadi,A.M., (2013), The hyper-Zagreb index of graph operations, Iran. J. Math. Chem., 4(2), pp. 213–220.
  • Su,G. and Xu,L., (2015), Topological indices of the line graph of subdivision graphs and their Schur- bounds, Appl. Math. Comput., 253, pp. 395–401.
  • Todeschini,R. and Consonni,V., (2000), Handbook of Molecular Descriptors, Wiley-VCH, Weinheim. [24] Vukicevic,D. and Furtula,B., (2009), Topological index based on the ratios of geometrical and arith- metical means of end-vertex degrees of edges, J. Math. Chem., 46, pp. 1369–1376.
  • Yu,G. and Feng,L., (2013), On connective eccentricity index of graphs, MATCH Commun. Math. Comput. Chem., 69, pp. 611-628.
  • Zhou,B. and Trinajsti´c,N., (2010), On general sum-connectivity index, J. Math. Chem., 47, pp. 210– 218.
Yıl 2016, Cilt: 6 Sayı: 2, 324 - 332, 01.12.2016

Öz

Kaynakça

  • Ashrafi,A.R., Doˇsli´c,T., and Hamzeh,A., (2010), The Zagreb coindices of graph operations, Discrete Appl. Math., 158, pp. 1571–1578.
  • Basavanagoud,B., Gutman,I. and Gali,C.S., (2015), On second Zagreb index and coindex of some derived graphs, Kragujevac J. Sci., 37, pp. 113–121.
  • Doˇsli´c,T., (2008), Vertex-weighted Wiener polynomials for composite graphs, Ars Mathematica Con- tempooranea, 1, pp. 66–80.
  • Estrada,E., Torres,L., Rodriguez,L. and Gutman,I., (1998), An atom-bond connectivity index: Mod- elling the enthalpy of formation of alkanes. Indian J. Chem., 37A, pp. 849–855.
  • Furtula,B., Graovac,A. and Vukiˇcevi´c,D., (2010), Augmented Zagreb index. Journal of Mathematical Chemistry., 48, pp. 370–380.
  • Ghorbani,M. and HosseinzadehM.A., (2010), Computing ABC4index of nanostar dendrimers, Opto- electron. Adv. Mater.-Rapid Commun., 4(9), pp. 1419–1422.
  • Graovac,A., Ghorbani,M. and Hosseinzadeh,M.A., Computing fifth geometric-arithmetic index for nanostar dendrimers., J. Math. Nanosci, 1, pp. 33–42.
  • Gutman,I. and Trinajsti´c,N., (1972), Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17, pp. 535–538.
  • Gutman,I., (1994), Selected properties of the Schultz molecular topological index, J. Chem. Inf. Com- put. Sci., 34, pp. 1087–1089.
  • Gutman,I., Furtula,B. and Elphick,C., (2014), Three new/old vertexdegreebased topological indices, MATCH Commun. Math. Comput. Chem., 72, pp. 617–632.
  • Hande,S.P., Jog,S.R., Ramane,H.S., Hampiholi,P.R., Gutman,I. and Durgi,B.S., (2013), Derived graphs of subdivision graphs, Kragujevac J. Sci., 37(2), pp. 319–323.
  • Harary,F., (1969), Graph Theory, Addison–Wesely, Reading.
  • Hosamani,S.M. and Gutman,I., (2014), Zagreb indices of transformation graphs and total transfor- mation graphs, Appl. Math. Comput., 247, pp. 1156-1160.
  • Hosamani,S.M. and Basavanagoud,B., (2015), New upper bounds for the first Zagreb index, MATCH Commun. Math. Comput. Chem., 74(1), pp. 97–101.
  • Li,X. and Shi,Y., (2008), A survey on the Randi´c index, MATCH Commun. Math. Comput. Chem., 59(1), pp. 127-156.
  • Li,X. and Zhao,H., (2004), Trees with the first three smallest and largest generalized topological indices, MATCH Commun. Math. Comput. Chem., 50, pp. 57-62.
  • Nadeem,M.F., Zafar,S. and Zahid,Z., (2015), Certain topological indicies of the line graph of subdiv- sion graphs, Appl. Math. Comput., (271), pp. 790–794.
  • Randi´c,M., (1974), On characterization of molecular branching, J. Am. Chem. Soc., 97, pp. 6609–6615. [19] Ranjini,P.S., Lokesha,V. and Cangul,I.N., (2011), On the Zagreb indices of the line graphs of the subdivision graphs, Appl. Math. Comput., 218, pp. 699–702.
  • Ranjini,P.S., Lokesha,V. and Rajan,M.A., (2011), On the Shultz index of the subdivision graphs, Adv. Stud. Contemp. Math., 21(3), pp. 279-290.
  • Shirdel,G.H., Rezapour,H. and Sayadi,A.M., (2013), The hyper-Zagreb index of graph operations, Iran. J. Math. Chem., 4(2), pp. 213–220.
  • Su,G. and Xu,L., (2015), Topological indices of the line graph of subdivision graphs and their Schur- bounds, Appl. Math. Comput., 253, pp. 395–401.
  • Todeschini,R. and Consonni,V., (2000), Handbook of Molecular Descriptors, Wiley-VCH, Weinheim. [24] Vukicevic,D. and Furtula,B., (2009), Topological index based on the ratios of geometrical and arith- metical means of end-vertex degrees of edges, J. Math. Chem., 46, pp. 1369–1376.
  • Yu,G. and Feng,L., (2013), On connective eccentricity index of graphs, MATCH Commun. Math. Comput. Chem., 69, pp. 611-628.
  • Zhou,B. and Trinajsti´c,N., (2010), On general sum-connectivity index, J. Math. Chem., 47, pp. 210– 218.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

S. M. Hosamani Bu kişi benim

V. Lokesha Bu kişi benim

I. N. Cangul Bu kişi benim

K. M. Devendraiah Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 6 Sayı: 2

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